Waddington (1968), for all his outstanding contributions to biology in the middle and later part of the 20th century, failed to mention the cell as a concept in his paper 'Main biological conceptions'. The cell to him was a reality, an object for investigation, a fact. Only such a fundamental notion can so present itself to one's consciousness that one considers it "something that goes without saying" - an objective phenomenon, like the sea or the stars. But the cell, a concept that took many years to emerge, was by no means an "obvious fact" to all concerned at the outset. The cell concept probably had a no less painful birth than many other concepts that now are considered fact, such as the heliocentric nature of our solar system (Galileo, 1612-32). That birth (not literally of the cell, but of the concept of the cell) has been the subject of much intensive research, compiled as one fascinating, highly erudite but complex treatise in Harris (2000). We might all concede that there is a "unit of life", and might be prepared to call it a cell, but there is no precise, unambiguous and generally agreed definition of "a cell".

Think about algebra: the number, as the simplest of all algebric concepts has no definition. In geometry, the dot has no definition. Therefore, in biology, the cell needs no definition.
Think of it like this: Anything with a membrane, cytoplasm and genome si a cell

"As a biologist, I firmly believe that when you're dead, you're dead. Except for what you live behind in history. That's the only afterlife" - J. Craig Venter

A number is a value representing the count of a group of units.
A point [dot] is a location in three dimensional space used to give positions for more complex units, for example, lines.

This argument is following the lines of Reductionism and Wholisitic science.

The cell is the basic unit of life--taken from modern Cell Theory

Dr. Matveev has a highly valid point. Remember our debates on whether or not viruses are alive? The definition of a cell must be refined because of this. Asking deeper questions, what is a membrane? If a membrane is a shell protecting the innards of a cell, then by all means, a virus is a cell. But if the definition of membrane is refined to a phospholipid bilayer, then viruses are ruled out. They have a protective shell...but it is not made of lipids...it is made of proteins.

Reading this thread and its attachment, my interest is highly piqued. Please keep us appraised on the events surrounding this research.